Chapter practice examination

Original untimed practice examination. Not a secure or official placement test.

Original untimed practice examination. Not a secure or official placement test. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.

Assessment · 24 questions

Questions

Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.

A1
A student answers the following question with “49 square units; 28 units”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A 8-by-6 rectangle has what area and what perimeter? Include units. (3 points)
Reveal explanation
Answer: 48 square units; 28 units
The suggested answer is not correct. Area counts square units: 8 × 6 = 48. Perimeter counts the boundary: 2(8+6) = 28. They have different units.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A2
A 8-by-4 rectangle has what area and what perimeter? Include units. (3 points)
Reveal explanation
Answer: 32 square units; 24 units
Area counts square units: 8 × 4 = 32. Perimeter counts the boundary: 2(8+4) = 24. They have different units.
Scoring: 1 point for area, 1 for perimeter, 1 for both appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A3
A tiled mat is 3 square units across and 5 square units down. How many unit squares cover it? (2 points)
Reveal explanation
Answer: 15 square units
There are 5 rows of 3 equal square units: 3 × 5 = 15 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A4
A rectangular fence is 4 cm long and 4 cm wide. What length of edging goes all the way around? (2 points)
Reveal explanation
Answer: 16 cm
Walk along every outer edge once: 4 + 4 + 4 + 4 = 16 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A5
A student answers the following question with “16 square units”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A rectangular garden covers 3 rows of 5 equal unit squares. Find its area. (3 points)
Reveal explanation
Answer: 15 square units
The suggested answer is not correct. There are 3 rows of 5 equal square units: 5 × 3 = 15 square units.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A6
A rectangle measures 7 cm by 3 cm. What is its perimeter? (2 points)
Reveal explanation
Answer: 20 cm
Walk along every outer edge once: 7 + 3 + 7 + 3 = 20 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A7
A tiled mat is 5 square units across and 4 square units down. How many unit squares cover it? (2 points)
Reveal explanation
Answer: 20 square units
There are 4 rows of 5 equal square units: 5 × 4 = 20 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A8
A rectangle is 7 unit squares across and 6 unit squares down. What is its area? (2 points)
Reveal explanation
Answer: 42 square units
There are 6 rows of 7 equal square units: 7 × 6 = 42 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A9
A student answers the following question with “25 square units”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A rectangle is 8 unit squares across and 3 unit squares down. What is its area? (3 points)
Reveal explanation
Answer: 24 square units
The suggested answer is not correct. There are 3 rows of 8 equal square units: 8 × 3 = 24 square units.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A10
A rectangle measures 8 cm by 5 cm. What is its perimeter? (2 points)
Reveal explanation
Answer: 26 cm
Walk along every outer edge once: 8 + 5 + 8 + 5 = 26 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A11
A rectangular garden covers 3 rows of 7 equal unit squares. Find its area. (2 points)
Reveal explanation
Answer: 21 square units
There are 3 rows of 7 equal square units: 7 × 3 = 21 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A12
A rectangle measures 6 cm by 5 cm. What is its perimeter? (2 points)
Reveal explanation
Answer: 22 cm
Walk along every outer edge once: 6 + 5 + 6 + 5 = 22 cm.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A13
A student answers the following question with “25 square units”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A rectangle is 6 unit squares across and 4 unit squares down. What is its area? (3 points)
Reveal explanation
Answer: 24 square units
The suggested answer is not correct. There are 4 rows of 6 equal square units: 6 × 4 = 24 square units.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A14
A 5-by-5 rectangle has a 1-by-2 corner removed. Find the remaining area in square units. (2 points)
Reveal explanation
Answer: 23 square units
Whole rectangle: 5 × 5 = 25. Missing corner: 1 × 2 = 2. Remaining: 25 − 2 = 23.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A15
A tiled mat is 4 square units across and 6 square units down. How many unit squares cover it? (2 points)
Reveal explanation
Answer: 24 square units
There are 6 rows of 4 equal square units: 4 × 6 = 24 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A16
A rectangular garden covers 6 rows of 4 equal unit squares. Find its area. (2 points)
Reveal explanation
Answer: 24 square units
There are 6 rows of 4 equal square units: 4 × 6 = 24 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A17
A student answers the following question with “17 cm”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A rectangular fence is 5 cm long and 3 cm wide. What length of edging goes all the way around? (3 points)
Reveal explanation
Answer: 16 cm
The suggested answer is not correct. Walk along every outer edge once: 5 + 3 + 5 + 3 = 16 cm.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A18
A rectangular garden covers 4 rows of 5 equal unit squares. Find its area. (2 points)
Reveal explanation
Answer: 20 square units
There are 4 rows of 5 equal square units: 5 × 4 = 20 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A19
A rectangle is 6 unit squares across and 2 unit squares down. What is its area? (2 points)
Reveal explanation
Answer: 12 square units
There are 2 rows of 6 equal square units: 6 × 2 = 12 square units.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A20
A 5-by-3 rectangle has what area and what perimeter? Include units. (3 points)
Reveal explanation
Answer: 15 square units; 16 units
Area counts square units: 5 × 3 = 15. Perimeter counts the boundary: 2(5+3) = 16. They have different units.
Scoring: 1 point for area, 1 for perimeter, 1 for both appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A21
A student answers the following question with “17 cm”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: A rectangular fence is 6 cm long and 2 cm wide. What length of edging goes all the way around? (3 points)
Reveal explanation
Answer: 16 cm
The suggested answer is not correct. Walk along every outer edge once: 6 + 2 + 6 + 2 = 16 cm.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
Square-unit grid; count only visible squares without gaps or overlap.
A22
A 3-by-3 rectangle has a 2-by-1 corner removed. Find the remaining area in square units. (2 points)
Reveal explanation
Answer: 7 square units
Whole rectangle: 3 × 3 = 9. Missing corner: 2 × 1 = 2. Remaining: 9 − 2 = 7.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
Square-unit grid; count only visible squares without gaps or overlap.
A23
A student says a rectangle with area 16 square units must have perimeter 16 units. Explain why this is not generally true using a 4-by-4 example. (3 points)
Reveal explanation
Answer: Perimeter 16 units
The area is 4 × 4 = 16 square units, but its perimeter is 2 × (4+4) = 16 units. Area and perimeter measure different things.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.
A24
A 3-by-4 rectangle and a 1-by-12 rectangle have the same area. Must they have the same perimeter? (3 points)
Reveal explanation
Answer: No
Both areas are equal, but different side dimensions usually give different boundary lengths.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.

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